Percentage Decrease Calculator
Enter an old value and a new value to see the percentage decrease, or take a percentage off any number. The answer updates as you type.
Percentage decrease from to
A decrease of 20.
Take % off
The percentage decrease formula
Percentage decrease = (old value − new value) ÷ old value × 100
You always divide by the old value, the one you started from. That is why a fall from 80 to 60 is 25%, while a rise from 60 back to 80 is about 33.3%.
Worked examples
Each row uses the formula above: the change is old minus new, and the percentage is that change divided by the old value.
| Old | New | Change | Decrease |
|---|---|---|---|
| 80 | 60 | 20 | 25% |
| 250 | 200 | 50 | 20% |
| 1,200 | 1,020 | 180 | 15% |
| 60 | 45 | 15 | 25% |
A jacket marked down from 250 to 200 has dropped by 50. Divide by 250 to get 0.2, then multiply by 100 for a 20% decrease.
Taking a percentage off instead
If you know the percentage and want the new number, multiply the original by 1 minus the rate as a decimal. Taking 25% off 60 gives 60 × 0.75 = 45. Taking 15% off 1,200 gives 1,200 × 0.85 = 1,020, which matches the table above.
Common mistakes
Dividing by the new value instead of the old one overstates the fall. Another is assuming that a percentage fall and the same percentage rise cancel out. They do not, because they are measured from different starting points.
FAQ
How do you calculate percentage decrease?
Subtract the new value from the old value, divide the result by the old value, then multiply by 100. Going from 80 to 60 is a fall of 20, and 20 ÷ 80 × 100 = 25%, so the decrease is 25%.
What is the percentage decrease formula?
Percentage decrease = (old value − new value) ÷ old value × 100. As with any percentage change, you divide by the original value.
How do I take a percentage off a number?
Multiply the number by 1 minus the percentage as a decimal. To take 25% off 60, multiply 60 by 0.75 to get 45. The second calculator above does this for you.
How do I find the original price before a discount?
Divide the sale price by 1 minus the discount rate. If a price is 48 after a 20% discount, the original was 48 ÷ 0.8 = 60. Adding 20% back onto 48 would give the wrong answer.
Why does a 20% rise followed by a 20% fall not return to the start?
Each percentage is worked out from a different base. 100 plus 20% is 120, and 20% of 120 is 24, which brings you down to 96. To get from 120 back to 100 you need a fall of about 16.7%.
Can a percentage decrease be more than 100%?
No, not for a value that cannot go below zero. A 100% decrease takes a value to zero. If the new value is higher than the old one, the calculator tells you it is an increase.
What is 30% off $80?
30% of $80 is $24, so the sale price is $56. In the second box, enter 30 and 80.
If a price falls 20% and then rises 20%, is it back to the start?
No. $100 falls to $80 and then rises 20% to $96, which is 4% below the starting price. The rise is calculated on the lower amount.
How do I find the original price from a discounted price?
Divide the sale price by 1 minus the discount as a decimal. If an item costs $75 after 25% off, the original price was $75 ÷ 0.75 = $100.
Why recovering from a loss takes a bigger gain
A percentage fall is measured against the old, higher value, but a recovery is measured against the new, lower one. That makes the gain needed to get back to where you started larger than the fall itself:
| Percentage drop | Remaining value of $100 | Gain needed to get back to $100 |
|---|---|---|
| 10% | $90.00 | 11.1% |
| 20% | $80.00 | 25.0% |
| 25% | $75.00 | 33.3% |
| 33% | $67.00 | 49.3% |
| 50% | $50.00 | 100.0% |
| 75% | $25.00 | 300.0% |
A 50% drop needs a 100% gain to recover. This is why large losses in investments, prices or sales are so hard to make up.
Combining discounts
When two discounts apply one after the other, the second takes its percentage from the already reduced price, so the total is less than the sum of the two.
| Discounts applied one after the other | Price of $100 item | Overall discount |
|---|---|---|
| 20% then 10% | $72.00 | 28% |
| 30% then 20% | $56.00 | 44% |
| 50% then 25% | $37.50 | 62.5% |
| 10% three times | $72.90 | 27.1% |
A 20% discount followed by 10% off is a 28% discount overall, and not 30%. Check how a store applies its coupon codes.
Working backwards to the original price
If you know the sale price and the discount, divide by 1 minus the discount as a decimal.
| Sale price | Discount | Original price |
|---|---|---|
| $60.00 | 25% | $80.00 |
| $85.00 | 15% | $100.00 |
| $140.00 | 30% | $200.00 |
| $45.00 | 50% | $90.00 |
For example, a $60 price after a 25% discount was originally $60 ÷ 0.75 = $80.
Everyday uses
- Shopping. Work out the real saving on a sale and compare it with another offer.
- Weight and fitness. Express weight lost as a percentage of starting weight.
- Business. Measure falls in sales, traffic or costs from one period to the next.
- Budgeting. See how much your spending has dropped after a change.
For rises, use the percentage increase calculator.